Spectral norm of random Toeplitz matrices

Spectral norm of random Toeplitz matrices

In this work, we consider symmetric random Toeplitz matrices \(T_n\) generated by i.i.d. zero mean random variables \({X_k}\) satisfying the moment conditions: \(E|X_k|^2=1\) and \(\E|X_1|^n \le n^{\sqrt{n}}\) for all \(n\ge 3\). We prove that the largest eigenvalue of \(T_n\) scaled by \(\sqrt{n lo...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2013-01
1. Verfasser: Kharouf, Malika
Format: Artikel
Sprache:eng
Schlagworte:
Eigenvalues
Mathematical analysis
Matrix methods
Random variables
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In this work, we consider symmetric random Toeplitz matrices \(T_n\) generated by i.i.d. zero mean random variables \({X_k}\) satisfying the moment conditions: \(E|X_k|^2=1\) and \(\E|X_1|^n \le n^{\sqrt{n}}\) for all \(n\ge 3\). We prove that the largest eigenvalue of \(T_n\) scaled by \(\sqrt{n log(n)}\) converges almost surely to \(1\).
ISSN:2331-8422